Temporal autocorrelation and stochastic population growth

How much does environmental autocorrelation matter to the growth of structured populations in real life contexts? Interannual variances in vital rates certainly do, but it has been suggested that between‐year correlations may not. We present an analytical approximation to stochastic growth rate for multistate Markovian environments and show that it is accurate by testing it in two empirically based examples. We find that temporal autocorrelation has sizeable effect on growth rates of structured populations, larger in many cases than the effect of interannual variability. Our approximation defines a sensitivity to autocorrelated variability, showing how demographic damping and environmental pattern interact to determine a population's stochastic growth rate.     

Quantitative trait loci for growth and body size in the nine‐spined stickleback Pungitius pungitius L.

Body size is an ecologically important trait shown to be genetically variable both within and among different animal populations as revealed by quantitative genetic studies. However, few studies have looked into underlying genetic architecture of body size variability in the wild using genetic mapping methods. With the aid of quantitative trait loci (QTL) analyses based on 226 microsatellite markers, we mapped body size and growth rate traits in the nine‐spined stickleback (Pungitius pungitius) using an F₂‐intercross (n = 283 offspring) between size‐divergent populations. In total, 17 QTL locations were detected. The proportion of phenotypic variation explained by individual body size‐related QTL ranged from 3% to 12% and those related to growth parameters and increments from 3% to 10%. Several of the detected QTL affected either early or late growth. These results provide a solid starting point for more in depth investigations of structure and function of genomic regions involved in determination of body size in this popular model of ecological and evolutionary research.     

Rainbow trout in seasonal environments: phenotypic trade‐offs across a gradient in winter duration

Survival through periods of resource scarcity depends on the balance between metabolic demands and energy storage. The opposing effects of predation and starvation mortality are predicted to result in trade‐offs between traits that optimize fitness during periods of resource plenty (e.g., during the growing season) and those that optimize fitness during periods of resource scarcity (e.g., during the winter). We conducted a common environment experiment with two genetically distinct strains of rainbow trout to investigate trade‐offs due to (1) the balance of growth and predation risk related to foraging rate during the growing season and (2) the allocation of energy to body size prior to the winter. Fry (age 0) from both strains were stocked into replicate natural lakes at low and high elevation that differed in winter duration (i.e., ice cover) by 59 days. Overwinter survival was lowest in the high‐elevation lakes for both strains. Activity rate and growth rate were highest at high elevation, but growing season survival did not differ between strains or between environments. Hence, we did not observe a trade‐off between growth and predation risk related to foraging rate. Growth rate also differed significantly between the strains across both environments, which suggests that growth rate is involved in local adaptation. There was not, however, a difference between strains or between environments in energy storage. Hence, we did not observe a trade‐off between growth and storage. Our findings suggest that intrinsic metabolic rate, which affects a trade‐off between growth rate and overwinter survival, may influence local adaptation in organisms that experience particularly harsh winter conditions (e.g., extended periods trapped beneath the ice in high‐elevation lakes) in some parts of their range.     

Some Consequences of Size Variability in Juvenile Prickly Sculpin, Cottus asper

Variation in size among fishes can have important ecological consequences. The origin and persistence of variation in size among a cohort of juvenile prickly sculpin, Cottus asper, was explored experimentally by manipulating the size variability in juvenile fish and the presence of conspecific adult fishes in a factorial design. I found that adult fish significantly suppressed the growth and survivorship of juveniles, while the variance treatment alone had no effect on growth or survivorship. The presence of adults was also associated with a decrease in size variability in the high variance treatment. An analysis of juvenile growth patterns revealed no evidence for size dependent growth or temporal correlations in growth (`growth autocorrelation'), and are consistent with a lack of amplification of size variance through time. Juvenile C. asper appear to have been feeding on a relatively homogeneous resource and utilizing those resources similarly. Thus, patterns of individual growth and the presence of adult conspecifics may both serve to dampen size differences in this coastal fish species.     

Variability in the growth rate of chub Leuciscus cephalus along a longitudinal river gradient

An increase in individual growth rate of chub Leuciscus cephalus along a longitudinal river gradient of the Rhône River basin was observed and supported by significant differences between mean growth rates of successive river size groups. The potential implications of the results for studies on species traits variability along large-scale environmental gradients are discussed.     

Can temporal covariation and autocorrelation in demographic rates affect population dynamics in a raptor species?

Theoretical studies suggest that temporal covariation among and temporal autocorrelation within demographic rates are important features of population dynamics. Yet, empirical studies have rarely focused on temporal covariation and autocorrelation limiting our understanding of these patterns in natural populations. This lack of knowledge restrains our ability to fully understand population dynamics and to make reliable population forecasts. In order to fill this gap, we used a long‐term monitoring (15 years) of a kestrel Falco tinnunculus population to investigate covariation and autocorrelation in survival and reproduction at the population level and their impact on population dynamics. Using Bayesian joint analyses, we found support for positive covariation between survival and reproduction, but weak autocorrelation through time. This positive covariation was stronger in juveniles compared with adults. As expected for a specialized predator, we found that the reproductive performance was strongly related to an index of vole abundance explaining 86% of the temporal variation. This very strong relationship suggests that the temporally variable prey abundance may drive the positive covariation between survival and reproduction in this kestrel population. Simulations suggested that the observed effect size of covariation could be strong enough to affect population dynamics. More generally, positive covariation and autocorrelation have a destabilizing effect increasing substantially the temporal variability of population size.     

Optimal Reproductive Strategy of Plants, with Special Reference to the Modes of Reproductive Resource Allocation

Abstract A growth model for reproductive energy allocation pattern and schedule is proposed. Assumptions are as follows: (1) the assimilation rate for an individual is given by a logistic curve of vegetative dry weight; (2) size variability is expressed by the parameter W of the logistic curve (asymptotic value of vegetative dry weight); (3) a plant controls allocation of the assimilate to vegetative and reproductive structures so as to maximize the reproductive energy investment at the end of the growth period. The models were analyzed in comparison with field and experimental observations and gave reasonable explanations for the reproductive allocation pattern of individuals which reflects ecological preferences and life history characteristics, such as environmental conditions of habitats (stable or changing), length of life span (annual, biennial or perennial) and growth form (erectophile or planophile). Decreasing RA (reproductive allocation) with individual size and delayed switchover time from vegetative to reproductive growth were found in plants which occur in stable environments and have a more or less fixed growth period; in those which occur in changing environments where growth period depends on individual size, RAs that remain constant or increase with variations in individual size and early switchover time were detected. Most perennials conform to the former case, but annuals and biennials conform to the latter case. Under extremely overcrowded conditions, planophiles, which are much more subject to crowding effect than erectophiles, tend to have increasing RA with increasing size, while erectophiles tend to have almost constant RA irrespective of size. These trends are discussed in the light of the life history characteristics and ecological distribution of plant species studied.     

Quantifying climate–growth relationships at the stand level in a mature mixed‐species conifer forest

A range of environmental factors regulate tree growth; however, climate is generally thought to most strongly influence year‐to‐year variability in growth. Numerous dendrochronological (tree‐ring) studies have identified climate factors that influence year‐to‐year variability in growth for given tree species and location. However, traditional dendrochronology methods have limitations that prevent them from adequately assessing stand‐level (as opposed to species‐level) growth. We argue that stand‐level growth analyses provide a more meaningful assessment of forest response to climate fluctuations, as well as the management options that may be employed to sustain forest productivity. Working in a mature, mixed‐species stand at the Howland Research Forest of central Maine, USA, we used two alternatives to traditional dendrochronological analyses by (1) selecting trees for coring using a stratified (by size and species), random sampling method that ensures a representative sample of the stand, and (2) converting ring widths to biomass increments, which once summed, produced a representation of stand‐level growth, while maintaining species identities or canopy position if needed. We then tested the relative influence of seasonal climate variables on year‐to‐year variability in the biomass increment using generalized least squares regression, while accounting for temporal autocorrelation. Our results indicate that stand‐level growth responded most strongly to previous summer and current spring climate variables, resulting from a combination of individualistic climate responses occurring at the species‐ and canopy‐position level. Our climate models were better fit to stand‐level biomass increment than to species‐level or canopy‐position summaries. The relative growth responses (i.e., percent change) predicted from the most influential climate variables indicate stand‐level growth varies less from to year‐to‐year than species‐level or canopy‐position growth responses. By assessing stand‐level growth response to climate, we provide an alternative perspective on climate–growth relationships of forests, improving our understanding of forest growth dynamics under a fluctuating climate.     

Microbial growth dynamics on the basis of individual budgets

The popular theories for microbial dynamics by Monod, Pirt and Droop are shown to be special cases of a model for individual budgets, in which growth and maintenance are on the expense of reserve materials. The dynamics of reserve materials is a first order process with a relaxation time proportional to cell length; maintenance is proportional to cell volume, and uptake, which depends hyperbolically on substrate density, is proportional to cell volume as well. Because of the latter, population dynamics depends on the behaviour of the individuals in a simple way, such that the cell volume distribution has no quantitative effect.When uptake is proportional to the surface area of the cell, which is realistic from a physical point of view, the relation between the individual level and the population one becomes more complicated and the cell size and shape distribution affects population dynamics. It is shown how the changing shape of rods modifies uptake and, consequently, growth.The concept of energy conductance, defined as the ratio, of the maximum surface area specific uptake and the volume specific energy reserve has been introduced in the analysis of microbial dynamics. The first tentative results indicate that the value for E. coli is close to the mean value for a wide variety of animals.Properties of the model for cell suspension at constant substrate densities are analyzed and tested against a variety of experimental data from the literature on both the individual and the population level.     

The evolution of growth trajectories: what limits growth rate?

According to life‐history theory, growth rates are subject to strong directional selection due to reproductive and survival advantages associated with large adult body size. Yet, growth is commonly observed to occur at rates lower than the maximum that is physiologically possible and intrinsic growth rates often vary among populations. This implies that slower growth is favoured under certain conditions. Realized growth rate is thus the result of a compromise between the costs and advantages of growing rapidly, and the optimal rate of growth is not equivalent to the fundamental maximum rate. The ecological and evolutionary factors influencing growth rate are reviewed, with particular emphasis on how growth might be constrained by direct fitness costs. Costs of accelerating growth might contribute to the variance in fitness that is not attributable to age or size at maturity, as well as to the variation in life‐history strategies observed within and among species. Two main approaches have been taken to study the fitness trade‐offs relating to growth rate. First, environmental manipulations can be used to produce treatment groups with different rates of growth. Second, common garden experiments can be used to compare fitness correlates among populations with different intrinsic growth rates. Data from these studies reveal a number of potential costs for growth over both the short and long term. In order to acquire the energy needed for faster growth, animals must increase food intake. Accordingly, in many taxa, the major constraint on growth rate appears to arise from the trade‐off between predation risk and foraging effort. However, growth rates are also frequently observed to be submaximal in the absence of predation, suggesting that growth trajectories also impact fitness via other channels, such as the reallocation of finite resources between growth and other traits and functions. Despite the prevalence of submaximal growth, even when predators are absent, there is surprisingly little evidence to date demonstrating predator‐independent costs of growth acceleration. Evidence that does exist indicates that such costs may be most apparent under stressful conditions. Future studies should examine more closely the link between patterns of resource allocation to traits in the adult organism and lifetime fitness. Changes in body composition at maturation, for example, may determine the outcome of trade‐offs between reproduction and survival or between early and late reproduction. A number of design issues for studies investigating costs of growth that are imposed over the long term are discussed, along with suggestions for alternative approaches. Despite these issues, identifying costs of growth acceleration may fill a gap in our understanding of life‐history evolution: the relationships between growth rate, the environment, and fitness may contribute substantially to the diversification of life histories in nature.     

People, species richness and human population growth

Aim To investigate how the magnitude of conservation conflicts arising from positive relationships between human population size and species richness is altered during a period of marked human population growth (2% year^?1). Location South Africa. Methods Anuran and avian species richness were calculated from atlas distribution maps, and human population was measured in 1996 and 2001, all at a quarter‐degree resolution. We investigated the relationships between human population size in, and its change during, these two periods and environmental energy availability. We then investigated the nature of relationships between species richness and human population size in both time periods, and its change during them; these analyses were conducted both with and without taking environmental energy availability into account. Finally, we investigated the nature of the relationships between human population size, and its change, and the proportion of protected land. Analyses were conducted both without and with taking spatial autocorrelation into account; the latter was achieved using mixed models that fitted a spatial covariance structure to the data. Results Change in human population size between 1996 and 2001 exhibited marked spatial variation, with both large increases and decreases, but was poorly correlated with environmental energy availability. The nature of the relationship between human population size and environmental energy availability did not, however, exhibit statistically significant differences regardless of whether the former was measured in 1996 or 2001. Similarly, relationships between species richness and human population size did not exhibit significant differences between the two periods. The strengths of the species–human relationships were markedly reduced when energy availability was taken into account. Change in human population size was poorly correlated with species richness. The proportion of protected land was negatively, albeit rather weakly, correlated with human population size in 1996 and 2001, and with its change between these two periods. Main conclusions Positive species–human relationships arise largely, but not entirely, because both species richness and human population size exhibit similar responses to environmental energy availability. During a period of rapid human population growth, and marked changes in the spatial variation in human population size, positive correlations remained between human population size and both anuran and avian species richness. The slope of these correlations did not, however, alter, and the most species‐rich areas are not those with the largest increases in human population. Despite marked population growth, the magnitude of conservation conflicts arising from positive species–human relationships thus appears to have remained largely unchanged.     

Linking frequencies of acorn masting in temperate forests to long-term population growth rates in a songbird: the veery (Catharus fuscescens)

Many terrestrial ecosystems are characterized by intermittent production of abundant resources for consumers, termed pulsed resources. The impact of resource pulses on populations downwind of the initial pulse are only beginning to be characterized, while the relationship between the frequencies of pulses and the long‐term growth rate of affected species is unknown. I monitored the reproductive success of veeries (Catharus fuscescens) breeding in oak‐dominated forest in southeastern New York State from 1998 to 2002. During this time veeries experienced high interannual variability in growth rates as a consequence of trophic cascades stemming from pulsed production of acorns. Rodent populations that benefited from acorns also depredated veery nests, while raptors that increased in response to rodent outbreaks are major predators on adult and juvenile birds. Veeries may recoup losses following low to moderate acorn crops that lead to rodent population declines. Thus, veeries fluctuate between years of positive and negative growth rate, however, long‐term population trends, and thus true source‐sink designation, cannot be made until the frequency of various year types is characterized. I simulated long‐term growth rates using reproductive parameters estimated from field studies and survivorship data from the literature. Simulations suggest that variability in the frequency of masting events in oaks can lead to ～10% fluctuation in long‐term growth rates in veeries. These studies suggest that temporal variability in masting dynamics has the potential to substantially influence songbird population trends. Furthermore, spatial variability in masting characteristics (e.g. the frequency of masting events and/or the size of seed crops) may greatly contribute to regional differences in songbird population trends. Because even less is known about the relationship between sizes of acorn crops and songbird populations, the influence of pulses in seed production on songbird population dynamics is likely to be underestimated.     

Experimental and model analyses of the effects of competition on individual size variation in wood frog (Rana sylvatica) tadpoles

1. Size variation is a ubiquitous feature of animal populations and is predicted to strongly influence species abundance and dynamics; however, the factors that determine size variation are not well understood. 2. In a mesocosm experiment, we found that the relationship between mean and variation in wood frog (Rana sylvatica) tadpole size is qualitatively different at different levels of competition created by manipulating resource supply rates or tadpole density. At low competition, relative size variation (as measured by the coefficient of variation) decreased as a function of mean size, while at high competition, relative size variation increased. Therefore, increased competition magnified differences in individual performance as measured by growth rate. 3. A model was developed to estimate the contribution of size-dependent factors (i.e. based on size alone) and size-independent factors (i.e. resulting from persistent inherent phenotypic differences other than size that affect growth) on the empirical patterns. 4. Model analysis of the low competition treatment indicated that size-dependent factors alone can describe the relationship between mean size and size variation. To fit the data, the size scaling exponent that describes the dependence of growth rate on size was determined. The estimated value, 0-83, is in the range of that derived from physiological studies. 5. At high competition, the model analysis indicated that individual differences in foraging ability, either size-based or due to inherent phenotypic differences (size-independent factors), were much more pronounced than at low competition. The model was used to quantify the changes in size-dependent or size-independent factors that underlie the effect of competition on size-variation. In contrast to results at low competition, parameters derived from physiological studies could not be used to describe the observed relationships. 6. Our experimental and model results elucidate the role of size-dependent and size-independent factors in the development of size variation, and highlight and quantify the context dependence of individual (intrapopulation) differences in competitive abilities.     

How far to go? Determinants of migration distance in land mammals

Animal migration is a global phenomenon, but few studies have examined the substantial within‐ and between‐species variation in migration distances. We built a global database of 94 land migrations of large mammalian herbivore populations ranging from 10 to 1638 km. We examined how resource availability, spatial scale of resource variability and body size affect migration distance among populations. Resource availability measured as normalised difference vegetation index had a strong negative effect, predicting a tenfold difference in migration distances between low‐ and high‐resource areas and explaining 23% of the variation in migration distances. We found a weak, positive effect of the spatial scale of resource variability but no effect of body size. Resource‐poor environments are known to increase the size of mammalian home ranges and territories. Here, we demonstrate that for migratory populations as well, animals living in resource‐poor environments travel farther to fulfil their resource needs.     

Age‐specific vibrissae growth rates: A tool for determining the timing of ecologically important events in Steller sea lions

Steller sea lions (SSL; Eumetopias jubatus) grow their vibrissae continually, providing a multiyear record suitable for ecological and physiological studies based on stable isotopes. An accurate age‐specific vibrissae growth rate is essential for registering a chronology along the length of the record, and for interpreting the timing of ecologically important events. We utilized four methods to estimate the growth rate of vibrissae in fetal, rookery pup, young‐of‐the‐year (YOY), yearling, subadult, and adult SSL. The majority of vibrissae were collected from SSL live‐captured in Alaska and Russia between 2000 and 2013 (n = 1,115), however, vibrissae were also collected from six adult SSL found dead on haul‐outs and rookeries during field excursions to increase the sample size of this underrepresented age group. Growth rates of vibrissae were generally slower in adult (0.44 ± 0.15 cm/mo) and subadult (0.61 ± 0.10 cm/mo) SSL than in YOY (0.87 ± 0.28 cm/mo) and fetal (0.73 ± 0.05 cm/mo) animals, but there was high individual variability in these growth rates within each age group. Some variability in vibrissae growth rates was attributed to the somatic growth rate of YOY sea lions between capture events (P = 0.014, r² = 0.206, n = 29).     

Variation in the temperature preference and growth rate of individual fish reconciles differences between two growth models

1. A growth model, originally developed for brown trout (Salmo trutta), has now been fitted to data for Atlantic salmon (S. salar) and stone‐loach (Barbatula barbatula) from English populations, and Arctic charr (Salvelinus alpinus) from Sweden. The model relates growth rate to temperature for a fish of standard size and the functional relationship has a triangular shape with a sharp peak at the optimal temperature for growth and zero growth at the base of the triangle. It was unsuitable for growth data for Norwegian salmon, and a curvilinear Ratkowsky model provided a better fit, though the experimental protocol was different in the Norwegian and English experiments. 2. The Norwegian salmon were kept in groups in each tank, had to compete for food, and had to be divided into slow, moderate and fast growers before the Ratkowsky model could be fitted. Each English salmon was kept in its own tank and fed individually. For replicate experiments, fish of similar size were selected. Variation among fish kept under similar conditions was therefore small, and the triangular model was essentially for individual fish, not groups of fish. 3. The present simulation study tests the hypothesis that individual differences in the growth response could account for the curvilinear growth‐temperature relationship for the Norwegian salmon. The triangular model was used to generate the growth response to temperature for a group of salmon, each fish having a slightly different temperature preference and growth rate. The result was a curvilinear response, well approximated by the Ratkowsky model (adjusted R² = 0.96). When the variability in individual temperature preference was increased, the Ratkowsky model was an even better fit (adjusted R² = 0.98). Therefore, the apparent discrepancy between the two models was reconciled by allowing for individual differences in temperature preference and growth rate within groups of fish.     

The temperature‐size rule in Daphnia magna across different genetic lines and ontogenetic stages: Multiple patterns and mechanisms

Ectotherms tend to grow faster, but reach a smaller size when reared under warmer conditions. This temperature‐size rule (TSR) is a widespread phenomenon. Despite the generality of this pattern, no general explanation has been found. We therefore tested the relative importance of two proposed mechanisms for the TSR: (1) a stronger increase in development rate relative to growth rate at higher temperatures, which would cause a smaller size at maturity, and (2) resource limitation placing stronger constraints on growth in large individuals at higher temperatures, which would cause problems with attaining a large size in warm conditions. We raised Daphnia magna at eight temperatures to assess their size at maturity, asymptotic size, and size of their offspring. We used three clonal lines that differed in asymptotic size and growth rate. A resource allocation model was developed and fitted to our empirical data to explore the effect of both mechanisms for the TSR. The genetic lines of D. magna showed different temperature dependence of growth and development rates resulting in different responses for size at maturity. Also, at warm temperatures, growth was constrained in large, but not in small individuals. The resource allocation model could fit these empirical data well. Based on our empirical results and model explorations, the TSR of D. magna at maturity is best explained by a stronger increase in development rate relative to growth rate at high temperature, and the TSR at asymptotic size is best explained by a size‐dependent and temperature‐dependent constraint on growth, although resource limitation could also affect size at maturity. In conclusion, the TSR can take different forms for offspring size, size at maturity, and asymptotic size and each form can arise from its own mechanism, which could be an essential step toward finding a solution to this century‐old puzzle.     

Temperature affects the partitioning of absorbed light energy in freshwater phytoplankton

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Simplifying a physiologically structured population model to a stage-structured biomass model

We formulate and analyze an archetypal consumer-resource model in terms of ordinary differential equations that consistently translates individual life history processes, in particular food-dependent growth in body size and stage-specific differences between juveniles and adults in resource use and mortality, to the population level. This stage-structured model is derived as an approximation to a physiologically structured population model, which accounts for a complete size-distribution of the consumer population and which is based on assumptions about the energy budget and size-dependent life history of individual consumers. The approximation ensures that under equilibrium conditions predictions of both models are completely identical. In addition we find that under non-equilibrium conditions the stage-structured model gives rise to dynamics that closely approximate the dynamics exhibited by the size-structured model, as long as adult consumers are superior foragers than juveniles with a higher mass-specific ingestion rate. When the mass-specific intake rate of juvenile consumers is higher, the size-structured model exhibits single-generation cycles, in which a single cohort of consumers dominates population dynamics throughout its life time and the population composition varies over time between a dominance by juveniles and adults, respectively. The stage-structured model does not capture these dynamics because it incorporates a distributed time delay between the birth and maturation of an individual organism in contrast to the size-structured model, in which maturation is a discrete event in individual life history. We investigate model dynamics with both semi-chemostat and logistic resource growth.     

Pooled energy budgets: Resituating human energy ‐allocation trade‐offs

Across taxa, many life‐history traits vary as a function of differences in body size. 1 - 5 Among primates, including humans, allometric relationships explain many trends in metabolic, growth, reproductive, and mortality rates. 6 - 8 But humans also deviate from nonhuman primates with respect to other developmental, reproductive, and parenting characteristics. 9 - 13 Broad relationships between life‐history traits and body size assume that energy expended in activity (foraging effort) is proportional to body size, and that energy available for growth and reproduction are equivalent. Because human subsistence and parenting are based on food sharing, and cooperation in labor and childrearing, the ways by which energy is acquired and allocated to alternate expenditures are expanded. We present a modification of the general allocation model to include a mechanism for these energy transfers. Our goal is to develop a framework that incorporates this mechanism and can explain the human life‐history paradox; that is, slow juvenile growth and rapid reproduction. We suggest that the central characteristics of human subsistence and energy transfer need to be accounted for in order to more fully appreciate human life‐history variability.